(i) The total area \(A\) is given by \(A = 2y \times 4x = 8xy\).

The total fencing used is given by the perimeter equation: \(10y + 12x = 480\).

Solving for \(y\) in terms of \(x\):

\(y = \frac{480 - 12x}{10} = 48 - 1.2x\).

Substitute \(y\) into the area equation:

\(A = 8x(48 - 1.2x) = 384x - 9.6x^2\).

(ii) To find the maximum area, differentiate \(A\) with respect to \(x\):

\(\frac{dA}{dx} = 384 - 19.2x\).

Set \(\frac{dA}{dx} = 0\) to find critical points:

\(384 - 19.2x = 0\).

Solving gives \(x = 20\).

Substitute \(x = 20\) back into the equation for \(y\):

\(y = 48 - 1.2 \times 20 = 24\).

Thus, the dimensions for maximum area are \(x = 20\) m and \(y = 24\) m.